Anagram-free colourings of graph subdivisions
An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. A vertex colouring of a graph is anagram-free if no subpath of the graph is an anagram. Anagram-free graph colouring was independently introduced by Kam\v{c}ev, {\L}uczak and Sudakov and ourselves. I...
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creator | Wilson, Tim E Wood, David R |
description | An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$
is a permutation of $W$. A vertex colouring of a graph is anagram-free if no
subpath of the graph is an anagram. Anagram-free graph colouring was
independently introduced by Kam\v{c}ev, {\L}uczak and Sudakov and ourselves. In
this paper we introduce the study of anagram-free colourings of graph
subdivisions. We show that every graph has an anagram-free $8$-colourable
subdivision. The number of division vertices per edge is exponential in the
number of edges. For trees, we construct anagram-free $10$-colourable
subdivisions with fewer division vertices per edge. Conversely, we prove lower
bounds, in terms of division vertices per edge, on the anagram-free chromatic
number for subdivisions of the complete graph and subdivisions of complete
trees of bounded degree. |
doi_str_mv | 10.48550/arxiv.1708.09571 |
format | Article |
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is a permutation of $W$. A vertex colouring of a graph is anagram-free if no
subpath of the graph is an anagram. Anagram-free graph colouring was
independently introduced by Kam\v{c}ev, {\L}uczak and Sudakov and ourselves. In
this paper we introduce the study of anagram-free colourings of graph
subdivisions. We show that every graph has an anagram-free $8$-colourable
subdivision. The number of division vertices per edge is exponential in the
number of edges. For trees, we construct anagram-free $10$-colourable
subdivisions with fewer division vertices per edge. Conversely, we prove lower
bounds, in terms of division vertices per edge, on the anagram-free chromatic
number for subdivisions of the complete graph and subdivisions of complete
trees of bounded degree.</description><identifier>DOI: 10.48550/arxiv.1708.09571</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2017-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1708.09571$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1708.09571$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Wilson, Tim E</creatorcontrib><creatorcontrib>Wood, David R</creatorcontrib><title>Anagram-free colourings of graph subdivisions</title><description>An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$
is a permutation of $W$. A vertex colouring of a graph is anagram-free if no
subpath of the graph is an anagram. Anagram-free graph colouring was
independently introduced by Kam\v{c}ev, {\L}uczak and Sudakov and ourselves. In
this paper we introduce the study of anagram-free colourings of graph
subdivisions. We show that every graph has an anagram-free $8$-colourable
subdivision. The number of division vertices per edge is exponential in the
number of edges. For trees, we construct anagram-free $10$-colourable
subdivisions with fewer division vertices per edge. Conversely, we prove lower
bounds, in terms of division vertices per edge, on the anagram-free chromatic
number for subdivisions of the complete graph and subdivisions of complete
trees of bounded degree.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzruOwjAQhWE3WyCWB6AiL-DsjGNn7BKh5SIh0dBHQ2KzliBBtkDL23PZrY70F0efEFOEUltj4IvTb7yVSGBLcIZwJOS852PiswzJ-6IdTsM1xf6YiyEUz375KfL10MVbzHHo86f4CHzKfvK_Y7Fffu8Xa7ndrTaL-VZyTShdzZ1jRYEqrTyhO2BrrEakStkADI4MgVG1hRZajZ3XttbKKusDaN9VYzH7u317m0uKZ0735uVu3u7qASXjO80</recordid><startdate>20170831</startdate><enddate>20170831</enddate><creator>Wilson, Tim E</creator><creator>Wood, David R</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20170831</creationdate><title>Anagram-free colourings of graph subdivisions</title><author>Wilson, Tim E ; Wood, David R</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-96ad9a27f7342e719b1c584117328f0a09757052680c0c41de48642828ef04ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Wilson, Tim E</creatorcontrib><creatorcontrib>Wood, David R</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Wilson, Tim E</au><au>Wood, David R</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Anagram-free colourings of graph subdivisions</atitle><date>2017-08-31</date><risdate>2017</risdate><abstract>An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$
is a permutation of $W$. A vertex colouring of a graph is anagram-free if no
subpath of the graph is an anagram. Anagram-free graph colouring was
independently introduced by Kam\v{c}ev, {\L}uczak and Sudakov and ourselves. In
this paper we introduce the study of anagram-free colourings of graph
subdivisions. We show that every graph has an anagram-free $8$-colourable
subdivision. The number of division vertices per edge is exponential in the
number of edges. For trees, we construct anagram-free $10$-colourable
subdivisions with fewer division vertices per edge. Conversely, we prove lower
bounds, in terms of division vertices per edge, on the anagram-free chromatic
number for subdivisions of the complete graph and subdivisions of complete
trees of bounded degree.</abstract><doi>10.48550/arxiv.1708.09571</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Combinatorics |
title | Anagram-free colourings of graph subdivisions |
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